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(4x+5)=12x^2+15x
We move all terms to the left:
(4x+5)-(12x^2+15x)=0
We get rid of parentheses
-12x^2+4x-15x+5=0
We add all the numbers together, and all the variables
-12x^2-11x+5=0
a = -12; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·(-12)·5
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-19}{2*-12}=\frac{-8}{-24} =1/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+19}{2*-12}=\frac{30}{-24} =-1+1/4 $
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